The pressure in upper crustal magma reservoirs is a key parameter for understanding pre-eruptive surface deformation and the governing processes leading to an eruptive crisis. Although much progress has been made in documenting pre-eruptive measurements, it remains difficult to incorporate measurements that span the full range of temporal scales of deformation (from seconds to years) using existing geophysical networks.

Instrumental limitations constitute a significant difficulty in the study of processes occurring over large frequency domains. Each geophysical measurement has its own sensitivity and thus is able to describe aspects of particular source mechanisms (Figure 2.2a). For instance, short period seismic monitoring is able to track magma motion (typically range) during seismic crises. However, the use of microseismic observations is limited during quiescence of volcanic activity. Broadband seismometers () have been successfully used to constrain magma flow in secondary conduits, dyke vibration and dyke propagation (Chouet, 1996).
Deformation survey networks (GPS, InSAR, extensometers, and tiltmeters) typically describe inter-crisis periods and highlight that the volcanic edifice is active between main flank eruptive events when the seismicity level is low. Deformation monitoring is thus complementary to seismic instrumentation. Despite the use of all techniques available from GPS to short-period seismometers, the period domain from 100 to 1000 seconds remains unfortunately inaccessible to all but very broadband seismometers (corner period seconds).
These instruments require high quality installations that are complex to complete in volcanic areas. Also, the integration of velocity into displacement time-series remains challenging, and distinguishing tilt from horizontal motion (Wielandt et al., 1999) is not always possible.
As a consequence, theoretical numerical models that simulate continuous magmatic injection cannot be fully tested. This limits the reliability of the prediction (both time and location) of eruptive events and explains why our understanding of processes is typically restricted to pressure drops assuming single geometries (location and shape) for the source.

Figure 2.2:
a) General sketch of the Piton de la Fournaise. Already successfully applied techniques are indicated on the sketch. b) Near infrared composite (432) of the Piton de la Fournaise volcano. Vegetated areas are red. The NDVI methodology cannot be applied on the upper part of the volcano, as there is a lack of vegetation. BAND 4 (Near infra-red, ) is the color red, BAND 3 (Visible red, ) is the color green, BAND 2 (Visible Green, ) is the color blue.

The creation of a physical model of a whole edifice will not be achieved until the unaccounted magma volumes injected in the volcano can be quantified properly.
Most techniques (deformation, concentration drops, etc.) evaluate the change in pressure and not the pressure relative to lithostatic pressure.
We estimate the absolute pressure in the magma chamber as a reference pressure for the whole edifice. In order to achieve this goal, we need to estimate the volumes intruded into or extruded from the magma chamber.
We propose to address both instrumental and theoretical limitations by defining a geophysical model centered on the upper magma reservoir.

Here, we integrate seismic data, supported by geodetic observations, in a multi-scale model of the pressure in the magma chamber over the last two decades for the Piton de la Fournaise. We set up a physical model able to integrate various techniques which is consistent with the wide range of length and time scales of signals recorded on the field.
As an example, we present an application (included in this framework) made at different time and space scales for different magmatic sources with different characteristic periods.

We reconstruct the pressure-history at Piton de la Fournaise (PdF) over the past two decades based on a collection of pressure drops to describe upper-crustal magma injection processes in relation to eruptive events. The choice of PdF as a study case is four-fold: First, this volcano is one of the few volcanic edifices with a very-broadband seismometer located within 10 km of the summit. Second, PdF volcano is minimally affected by tectonic stress or continental deformation. The maximal extension across the magmatic edifice was estimated at (Houlié, 2005). The upper magma chamber located at sea-level is thus not affected by a large flank deformation of the volcano.
Third, it has been one of the most active volcanoes during the last decade, with more than fifteen eruptions since 1998. And lastly, this volcano is vegetated enough (Figure 2.2b) to test the Normalized Difference Vegetation Index (NDVI) (Richardson, 1977) following guidelines defined previously (Houlié et al., 2006).

Figure 2.3:
When will the next flank eruption occur at Piton de la Fournaise? Projection of the Pressure during the next decade (). Assuming the pressurization rate would decrease to 20MPa/yr (period 1998-2000) or possibly to 5MPa/yr (back to the pre-1998 injection rate), the next eruptive flank event would occur between 2009 (E1) and 2012 (E2).

By proposing to model each event in the framework of the absolute pressure in the magma chamber, we hope to integrate models/datasets from various origins in order to set up a physical model of the volcano. The estimates provided in this work can be scaled according to any new available dataset (tiltmeters, degassing monitoring, etc.).

As a first step, we show that the injection rate in the upper magma chamber increased by at least a factor of 8 in two years (1999-2001), following the 1998 flank eruption. This result demonstrates the ability of the absolute pressure parameter to describe eruptive activity over decades using simple geometry reservoirs.

Additionally, computed amplitudes of the 2-year periodic magma bursts are consistent with previous long-term intrusion estimates and justify our choice of pressure of the magma chamber. The observed periodicity suggests an interaction between magma reservoirs and the changing stress state of the crust. This interaction was previously suggested (Aki and Ferrazzini, 2001). Representation of the volcano edifice mainly generated by monitoring habits that emphasize isolated events may be at odds with the physical model presented here.

The increased activity since 1998 may be preparing the next flank event along the fractures left open by the 1998 dyke injections. According to NDVI results, we encourage the community to also monitor the fractures formed by the 1998 eruption that have not emitted any magma yet.